Problem: Solve for t: $3 \cdot 3^t + \sqrt{9 \cdot 9^t} = 18$.
Answer: We note that $\sqrt{9 \cdot 9^t} = 3 \cdot 3^t$. The equation becomes: \begin{align*}
3 \cdot 3^t + 3 \cdot 3^t &= 18\\
\Rightarrow 6 \cdot 3^t &= 18 \\
\Rightarrow 3^t &= 3.
\end{align*}Therefore, $t = \boxed{1}$.